4 Linear inequality word problems[1].docx

Linear inequality word problems1. The following function gives the amount of money owed on a short term loan after t weeks. A(t)=1001.2512Which numerical expression best approximates the annual interest rate, excluding any late fees? (1 year=52 weeks.)A. 1-0.2526B. 0.2526-1C. 260.25D. 26 1.25Correct answer: B Difficulty level: 22. The rabbit population in an isolated forest rises and falls depending on the population of predators. Within the year 2014, the population, p, in thousands of rabbits mmm months after January 1, 2014 is:p=0.05(m1.5)(m8.5)+10The population reached ten thousand some time in February. At what other time, given as months after January 1, 2014, did the rabbit population reach ten thousand?Correct answer: 8.5 Difficulty level: 23. The hang time of a football is the amount of time the football stays in the air after being kicked. The height, in meters, of the football above the ground at time t can be modeled by the quadratic function:ht=-4.9t2+19.6tWhich of the following equivalent expressions displays the hang time of the football as a constant or coefficient?A. -4.9(t-2)2+19.6B. -4.9t(t-4)C. -4.9t-32-9.8t+44.1D. -4.9t-12+9.8t+4.9Correct answer: B Difficulty level: 24. Kaia throws a stone vertically upward from a bridge. The height, in meters, of the stone above the water at time t can be modeled by the quadratic function:h(t)=-4.9t2+9.8t+39.2After how many seconds does the stone hit the water?A. 1 secondB. 2 secondsC. 4 secondsD. 8 secondsCorrect answer: C Difficulty level: 25. More than 450 students traveled to a state park for a field trip. The school allowed 6 students to travel by car, and the rest traveled on 11 buses, each of which held the same number of students. If there were s students in each bus, which inequality best represents this situation?A. 11s+6450B. 11s+6450D. 6s+11450Correct answer: A Difficulty level: 26. A barber charges $12 for a haircut. His operating expenses are, on average, $37 per day. He calculates his profit by subtracting his operating costs from the money he earns from the haircuts he gives. In a given day, the barber expects to make a profit of at least $86. If the barber gives h haircuts in a day, which inequality best models this situation?A. 12h-3786B. 12(h-37)86C. 12h+3786D. 12(h+37)86Correct answer: A Difficulty level: 27. A distributor ships DVDs to several stores. The shipping boxes contain several DVDs (in their cases) plus a layer of padding at each end of the box. The DVD cases and layers of padding can be arranged neatly inside each box. Each DVD case is 14 mm (millimeters) thick, each layer of padding is 10 mm thick, and the length of the interior of the box is 132 mm. If d represents the number of DVDs that the distributor can fit into one box with two layers of padding, which of the following inequalities best models the situation?A. 10d+14132B. 14d+20132C. 20d+14132D. 14d+10132Correct answer: B Difficulty level: 28. To rent a car for one week, a car rental company charges a $200 base price as well as $0.45 per mile. Jennifer will rent a vehicle at this company, but she has a $275 budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget?A. 166 milesB. 167 milesC. 168 milesD. 169 milesCorrect answer: A Difficulty level: 29. Woo-Jin would like to bring several books from his favorite series in his backpack. The backpack can hold up to a depth of 1012 inches of materials. Woo-Jins laptop and a notebook fill a total of 3 inches of that depth. Each book would fill 1.5 inches of the depth of the backpack. Only one stack of books can fit the height and width of the backpack. If x represents the number of books that Woo-Jin could carry in his backpack, which of the following inequalities best models the situation described above?A. 3+1.5x10.5B. 3+1.5x10.5C. 3x+1.56.0B. 8.3-0.3(t-2000)6.0C. 8.3-0.3t6.0D. 8.3-0.3(t-2000)0 representing north and y11B. c41B. p54C. p72D. p90Correct answer: C Difficulty level: 229. Arianna and Hannah are conducting an experiment to test the difference threshold for sense of touch on the forehead. For trial 1, Hannah closes her eyes while Arianna gently touches 2 paperclip points 3 millimeters (mm) apart on Hannahs forehead. Then Hannah reports whether she could feel 1 or 2 points. For each of the next trials, Arianna and Hannah repeat this process, each time with the points 2 more mm apart. Hannah reports feeling 1 point until the points are 15mm apart, when she begins reporting that she feels 2 points. Which inequality best represents the trial numbers in which Hannah feels 2 points?A. t6B. t6C. t7D. t7Correct answer: C Difficulty level: 230. Turkeys government requires at least a 23 majority of Parliament members to approve any constitutional changes. There are 550 seats in the Parliament. Of those, 313 of the seats are occupied by members who have pledged to support a particular constitutional change. Which inequality represents the number of additional Parliament members, m, who would need to support the constitutional change to achieve the required majority?A. m53.6B. m158C. m303D. m366.6Correct answer: A Difficulty level: 231. In one state, a minimum of 246,400 valid signatures on a petition is required to get a voter initiative added to a state-wide ballot. The signature collectors can fit 25 signatures per page. They estimate that 61,600 of the signatures that they collect will not be valid (because of being duplicates, incomplete, or unregistered voters). If p represents the number of pages of signatures which the signature collectors should collect in order to get the voter initiative added to the ballot, which of the following inequalities best models the situation described above?A. 25p+61,600246,400B. 25p+61,600246,400C. 25p-61,600246,400D. 25p-61,600246,400Correct answer: C Difficulty level: 232. When police analyze the broken glass at a scene, it helps them reconstruct the situation. Headlight glass is much less dense than the window glass. The headlight glass will be 1.5 grams per milliliter or less. A police officer determines that a fragment of glass displaces 10.5mLof water. Use the formula density=massvolume. Which inequality best shows the possible mass, m, in grams of the fragment if it is headlight glass?A. m7B. m7C. m15.75D. m15.75Correct answer: D Difficulty level: 233. Jennifer wants to spend no more than $300 on school clothes. She spends $75 on a jacket and wants to buy some shirts that are on sale for $10 each. Which inequality represents the number, s, of shirts Jennifer can buy?A. s30C. s37D. s38Correct answer: A Difficulty level: 334. Teddy is delivering boxes of paper to each floor of an office building. Each box weighs 56 pounds, and Teddy himself weighs 140 pounds. If the maximum capacity of an elevator is 2,000 pounds, or one ton, which of the following inequalities describes how many b boxes Teddy can safely take on each elevator trip without going over the capacity?A. b32B. b32C. b33D. b33Correct answer: D Difficulty level: 335. A small airplane can carry less than 1050 pounds of luggage and mail. Tuesdays load of mail weighs 490 pounds. If each passenger brings 70 pounds of luggage, what is the greatest possible number of passengers that can travel on the airplane on Tuesday?A. 7B. 8C. 14D. 15Correct answer: A Difficulty level: 336. Trevon is going to buy a coat and a hat. The coat costs 3 times as much as the hat. He must spend less than $94. If the cost of the hat costs x dollars, which inequality best models this situation?A. 3x94C. 4x94Correct answer: C Difficulty level: 337. A shipping company charges $3.46 for the first pound of a package and $1.53 for each additional pound of the package. If Robin wants to spend under $100 on shipping, which inequality best represents how many pounds, p, Robin can have in her particular package?A. 3.46+1.53p100B. 3.46+1.53(p-1)100C. 3.46+1.53p-1100D. 3.46(p-1)+1.5326C. 2(t-1)+1026D. 2(t-1)+1026Correct answer: D Difficulty level: 443. A college student has equally weighted exam grades of 71, 83, and 90 on three 100-point exams. The student has one more 100-point exam that counts toward